An electron in the field of a slow surface harmonic of diffraction radiation in nonrelativistic free electron lasers - Quantum theory

A solution is presented for the nonstationary problem of electron diffraction by a potential that is periodic along the longitudinal coordinate and exponentially decreasing along the transverse coordinate. A theory is developed for the parametric quantum-mechanical resonance of a particle in the field of a surface diffraction radiation harmonic. The wave function and the electron energy spectrum are determined.